How to make ‘more’ better? Principles for effective use of multiple representations to enhance students’ learning about fractions

A metacognitive intervention for teaching fractions to students with or at-risk for learning disabilities in mathematics

“…In the third stage of SRSD, students continue to observe the teacher and peers as they progress to the emulation level of the development of self-regulation by imitating the teacher's behaviors as he or she models each step of the FACT + R 2 C 2 strategy to solve problems using multiple representations, such as the concrete-representational-abstract (CRA) sequence. Using multiple representations has received considerable empirical support, particularly in the domain of fractions, and CRA has been shown to be particularly effective with students with or at risk for MLD (Agrawal and Morin 2016;Carbonneau et al 2013;Rau and Matthews 2017). With repeated observation and emulation of the teacher's behaviors of the FACT + R 2 C 2 components and CRA instruction, students begin to own the strategy by developing closer and closer approximations of those behaviors (Schunk and Zimmerman, 2007).…”

3D Page-Flipped Worksheet on Impulse-Momentum to Develop Students' Scientific Communication Skills

“…The ability to use multiple representations supports multiple intelligences of students, and this claim has been confirmed by some studies which concluded that there is no single representation to describe all aspects of mathematical concepts, instruction in understanding the concept typically uses multiple representations. The results suggested that multiple representations can have significant benefits for student learning (Hubber et al, 2010;Rau et al, 2014;Rau & Matthews, 2017).…”

“…The two sample answers show different representational and argumentative skills. According to Rau & Matthews (2017), there are four elements of representations that must be achie-ved including (1) visual understanding; (2) visual fluency; (3) the connectional comprehension; and (4) the connectional fluency. Student A was able to construct three forms of representation, i.e., images, graphics, and mathematics.…”

Three types of mathematical representational translations: Comparing empirical and theoretical results

“…There is general agreement regarding the importance of representational translation fluency in mathematical comprehension and problem‐solving success (Adu‐Gyamfi, Bossé, & Chandler, ; Ainsworth, ; Common Core State Standards Initiative [CCSSI], ; National Council of Teachers of Mathematics [NCTM], , ). It is believed that flexibility in translating among multiple mathematical representations is the means through which a student may come to: grasp a concept or mathematical processes; pass from one representation to another; know the possibilities, limits, and effectiveness of each representation; and reject one representation in order to select a more appropriate representation in a given problematic situation and know the reason for the choice (Berthold & Renkl, ; Even, ; Janvier, ; Rau & Matthews, ).…”